Re: Define the intersection points of polynomials

First of all taking one quadratic at at a time I cannot uniquely determine the other two coefficients just because I know the first one and a point.

If I told you that the the coefficient of x^2 was 2 and the point it passed through was (5,28) you would end up with this.

2x^2 + a*x + b = 28

50 + 5a + b = -22

5a + b = - 22

I am stuck. This has an infinite number of solutions for a and b.

The next quadratic will yield another 2 variables c and d. Coupled with the 4 other variables that define the unknown points we have maybe 4 equations and 8 unknowns. An overdetermined set. This spells doom for a unique solution.

I think I need more relationships between the points and the quadratics.

In mathematics, you don't understand things. You just get used to them.

Re: Define the intersection points of polynomials

Hi;

Hold on. There are many interpolation formulas, as a matter of fact in the old days you were not considered a mathematician unless you discovered one.

The fact is you are going to end up with variables a,b,c,d,x0,y0,x1,y1 and we know few facts about them. What relationships we do know will amount to 4 equations in 8 unknowns. Even if these were linear which they are not we would not be able to come up with a unique solution. Interpolation will not help us out. I can get the solutions using mathematica. They will be large because they will have a lot of variables left in them.

Is there anymore that you can provide me, no matter how tiny?

In mathematics, you don't understand things. You just get used to them.

Re: Define the intersection points of polynomials

Re: Define the intersection points of polynomials

You want A, B in my drawing. Therefore you (x0,y0) and (x1,y1) that is 4 variables. To have a chance at getting those 4 as a number I need 4 equations. Then to get the 2 polynomials I need 4 more equations.

I need 8 equations to determine the uniquely. To give you answers that are numbers.

In mathematics, you don't understand things. You just get used to them.

Re: Define the intersection points of polynomials

I have a feeling that the intersections can be determined. You can set up three equations in x0,y0,x1,y1,a12, and a13. Then each three new equations add just 2 new variables, ai2 and ai3. So, with 12 equations and 12 variables, there is aa chance that the system will be determined.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.